If we are at Faisal Masjid, Islamabad and we want to move to Blue Area, Islamabad by searching on Google Maps as shown in figure 2.5 (a), we get a twisted path, showing us the way to reach our destination. However, the straight path as shown in figure 2.5 (b) can be shorter.
'The length of the path traveled between two positions is called distance.'Distance has no direction and therefore it is a scalar quantity. Distance is usually denoted by \( \Delta x, \Delta r, \Delta s, \Delta d \) or \( \Delta l \), and has SI unit as metre (m).
'The shortest distance from the initial position to the final position (or straight directed distance) is called displacement.'Displacement has direction and therefore it is a vector quantity. Displacement has SI unit as metre (same as length).
If an object moves, then the object's position changes. This change in position vector \( \Delta d \) of an object, from initial position \( d_1 \) to final position \( d_2 \), is known as displacement as shown in figure 2.6 (b). Mathematically:
POINT TO PONDER
\( \Delta d = d_2 - d_1 \)
Here we used the symbol \( \Delta \) (Greek letter delta) for change in position; however, it is used to represent a 'change in' any quantity. For example, elapsed time \( \Delta t \) is the change in (or the difference between) the ending time \( t_2 \) and beginning time \( t_1 \):
\( \Delta t = t_2 - t_1 \)
If on a 400 m running track your starting point and ending point are the same, how much distance have you covered? What is your displacement?
Can displacement be greater than distance?
Can distance and displacement be equal?